Least Common Multiple (LCM) of 103 and 122
The least common multiple (LCM) of 103 and 122 is 12566.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 103 and 122?
First, calculate the GCD of 103 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 122 = 0 remainder 103 |
| 2 | 122 ÷ 103 = 1 remainder 19 |
| 3 | 103 ÷ 19 = 5 remainder 8 |
| 4 | 19 ÷ 8 = 2 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 164 | 27716 |
| 107 and 86 | 9202 |
| 14 and 58 | 406 |
| 26 and 152 | 1976 |
| 28 and 45 | 1260 |